Average Distance Between Points On or In a Circle

I recently came across an interesting math problem on youtube (why youtube keeps showing me these when I’m watching cooking shows, I’ll never understand, but I digress).  What is the average distance between two random points on a circle?  This can also be expanded to ask what is the average distance between two random points inside a circle?  Now of course I’m not going to sit down and do lots of math to figure this out, but it is a kinda interesting problem for a monte carlo simulation.  So I dusted the python off and went to work.

Continue reading “Average Distance Between Points On or In a Circle”

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Riddler Classic – 10-14-2016 – Arbitraria

Here’s my solution to this weeks Riddler Classic puzzle from FiveThirtyEight.  Here’s the question: “While traveling in the Kingdom of Arbitraria, you are accused of a heinous crime. Arbitraria decides who’s guilty or innocent not through a court system, but a board game. It’s played on a simple board: a track with sequential spaces numbered from 0 to 1,000. The zero space is marked “start,” and your token is placed on it. You are handed a fair six-sided die and three coins. You are allowed to place the coins on three different (nonzero) spaces. Once placed, the coins may not be moved. Continue reading “Riddler Classic – 10-14-2016 – Arbitraria”